Chemical, Biological and Environmental Engineering A Few Comments About Fusion

Advanced Materials and Sustainable Energy Lab CBEE Binding Energy Energy released when nucleus created from protons and neutrons Larger binding energy per nucleon means more stable nucleus

Advanced Materials and Sustainable Energy Lab CBEE Fusion vs. Fission Fusion Fission

Advanced Materials and Sustainable Energy Lab CBEE Relevant fusion reactions

Advanced Materials and Sustainable Energy Lab CBEE Calculation of energy released Released energy follows from the mass deficit. Consider the reaction Masses of products are The mass deficit (Total mass before minus total mass after) for reaction is

Advanced Materials and Sustainable Energy Lab CBEE Energy then follows from Einstein’s formula Physicist’s unit of energy is electron volt (eV) (kilo-electron volt, keV; mega-electron volt MeV) Calculation of released energy

Advanced Materials and Sustainable Energy Lab CBEE Energy released by 1kg of D-T mixture 1 kg of a Deuterium/Tritium mixture would allow for a number of fusion reactions N This would generate If released over 24h, this is around 4 GW

Advanced Materials and Sustainable Energy Lab CBEE Availability of the fuel Natural abundance of D is 0.015% of all H (1 in 6700) However, at current rate of energy use there is enough H in the ocean for years Deuterium is also very easy to separate (i.e., cheap) Tritium is unstable with a half age of 12.3 years There is virtually no naturally occuring Tritium

Advanced Materials and Sustainable Energy Lab CBEE Availability of the fuel: T Tritium can be bred from Lithium Note that the neutron released in the D-T fusion reaction can be used for this purpose Enough Lithium on land for 10k to 30k years at low cost If the oceans included, enough Li for 10 7 years

Advanced Materials and Sustainable Energy Lab CBEE Why fusion …. A large amount of fuel is available, at a very low cost The fuel is available in all locations of the earth. Like fission, fusion is CO 2 neutral Fusion would yield only a small quantity of high level radioactive waste. There is only a small threat to non-proliferation of weapon material

Advanced Materials and Sustainable Energy Lab CBEE But... An energy producing working concept is yet to be demonstrated. The operation of a fusion reactor is hindered by several difficult (and rather interesting) physics phenomena Also bear in mind that the cost argument thus far focuses on the fuel only However, the cost of the energy is largely determined by the cost of the reactor...

Advanced Materials and Sustainable Energy Lab CBEE Distribution of energy over the products Energy released as kinetic energy of products Kinetic energy is not equally distributed: Since both energy and momentum are conserved You can solve for the energy in He and n Therefore n has 80% of energy and He has 20%

Advanced Materials and Sustainable Energy Lab CBEE Key problem of fusion …. Is the Coulomb barrier

Advanced Materials and Sustainable Energy Lab CBEE Reaction Cross Section Cross section is the effective area connected with the occurrence of the reaction If you are playing billiards, the cross section is  r 2 (with r the radius of the ball) Reaction cross section of relevant fusion reactions as function of energy. 1 barn = m 2

Advanced Materials and Sustainable Energy Lab CBEE Averaged reaction rate Imagine particle B bombarded by many particles A Number of collisions in  t is Bear in mind that  and v both depend on the energy (which is not the same for all particles) Cross section 

Advanced Materials and Sustainable Energy Lab CBEE Averaged reaction rate ….. The cross section must be averaged over energies of the particles. Assuming a Maxwell distribution

Advanced Materials and Sustainable Energy Lab CBEE Number of fusion reactions as function of average T Particle energy for average T (from Maxwell distribution) The reaction cross section The product of distribution and cross section (proportional to reaction rate)

Advanced Materials and Sustainable Energy Lab CBEE Compare the two Cross section as a function of energyAveraged reaction rate as a function of Temperature Averaged reaction rate has lesser dependence on energy

Advanced Materials and Sustainable Energy Lab CBEE Current fusion reactor concepts Based on a mixture of Deuterium and Tritium Designed to operate at around 10 keV (10 keV is equivalent to 100,000,000 K) Matter is in the plasma state (fully ionized) Both decisions are related to reaction cross section

Advanced Materials and Sustainable Energy Lab CBEE Implications from high temperature Temperature expresses an averaged energy. You can convert between K and eV (so 10 keV is 100 million Kelvin) The average thermal velocity at 10keV can be estimated as This is 10 6 m/s for Deuterium nuclei in plasma In a reactor of 10 m size the particles would be lost in 10  s... 1eV = K 1K=8.616x10 -5 eV

Advanced Materials and Sustainable Energy Lab CBEE Lawson criterion Derives conditions where production of fusion energy is possible We derived reaction rate of particle B due to particles A as In the case of more than one particle B we could get Remember we derived for a given temperature

Advanced Materials and Sustainable Energy Lab CBEE Fusion power The total fusion power then is the reaction rate times energy Using quasi-neutrality (Deuteriums and Tritiums are indistiguishable) For a 50-50% mixture of Deuterium and Tritium (n D =n T =1/2n)

Advanced Materials and Sustainable Energy Lab CBEE Fusion power At the relevant temperature range 6-20 keV the average cross section is Plugging in, the fusion power can then be expressed as

Advanced Materials and Sustainable Energy Lab CBEE To examine power economy if devices, power produced must be compared with power loss from the plasma For this we introduce the energy confinement time  E Ratio of energy content and power loss (e.g. Thermal conduction) Where W is the stored energy density The power loss

Advanced Materials and Sustainable Energy Lab CBEE Fusion Power to Heating Power ratio Combine this with the fusion power derived earlier This is called the “n-T-tau product” We can get two strategies for fusion energy from here: High n, low  E Low n, high  E (remember, temperature is fixed by cross section at 10 keV)

Advanced Materials and Sustainable Energy Lab CBEE Break-even and Ignition The break-even condition is defined as the state in which the total fusion power is equal to the heating power Note that some power could be externally supplied... Ignition is defined as the state in which the energy produced by the fusion reactions is sufficient to heat the plasma Remember that neutrons (80% of the energy) escape reactor; energy in He remains for plasma heating (20%)

Advanced Materials and Sustainable Energy Lab CBEE Inertial Containment Fusion: high n low  E Rapid compression and heating of a solid fuel (high n) pellet using laser or particle beams. Fusion occurs for a few mS... (low t) Idea is to obtain a sufficient amount of fusion reactions (P fusion ) to generate energy (P heat ) before the material flies apart

Advanced Materials and Sustainable Energy Lab CBEE

Advanced Materials and Sustainable Energy Lab CBEE Magnetic confinement: low n high  E In a plasma, all particles are charged If strong magnetic field applied, Lorentz force can be used to trap charged particles Force causes charged particles to gyrate around the field lines with a typical radius At 10 keV and 5 Tesla this radius of 4 mm for Deuterium and 0.07 mm for the electrons

Advanced Materials and Sustainable Energy Lab CBEE Tokamak / Stellarator

Advanced Materials and Sustainable Energy Lab CBEE Large Helical Device (LHD,Japan)

Advanced Materials and Sustainable Energy Lab CBEE Stellarator Inside the device it looks something like this Picture from LHD in JAPAN

Advanced Materials and Sustainable Energy Lab CBEE Tokamak progress as n-T-tau Current experiments are close to break- even The next step ITER is expected to operate above break-even but still below ignition

Advanced Materials and Sustainable Energy Lab CBEE ITER: International Thermonuclear Experimental Reactor 1985 partnership between EU, Russia (started by Soviet Union…), USA (left in 1999, returned in 2003), Japan, Canada (left in 2003), RoK (2003), India (2005), PRC (2007) Budget about G€10… (as in 10 billion euros) 50% from host “nation” (EU), remainder shared by others

Advanced Materials and Sustainable Energy Lab CBEE ITER Goals Achieve steady-state plasma with Q > 5 (5x break even) Momentarily achieve Q > 10 (ten times more thermal energy from fusion heating than is supplied by auxiliary heating Maintain fusion pulse for up to eight minutes. Develop technologies needed for fusion power plant Verify tritium breeding concepts. Refine neutron shield/heat conversion technology (most of energy in the D+T fusion reaction is released in the form of fast neutrons)